How does a general solution to the EFE behave near a singularity? The BKL conjecture states that a generic singularity is vacuum-dominated, local and oscillatory. However, numerical exploration discovered non-local inhomogeneous structures called spikes, whose exact solutions are discovered in 2008. Spikes provide a way to generate matter inhomogeneity in the alternative paradigm of inhomogeneous cosmology. The electromagnetic spike solutions are discovered recently.